Let's apply what we just learned to calculate the touching point.
We can use de Casteljau's algorithm to calculate curves using any number of points.
Let's take a closer look at the weights used during subdivision. Do we have to be careful when selecting weights?
Let's look more closely at how light bounces when it strikes an object. We'll cover reflected and refracted rays.
Are we really creating parabolic curves using this construction? Let's gain some insight first.
Use an array to store many objects as well as create any shape you can imagine. Click here to review objects.
Now you can start scaling your shapes to make your lamp look younger.
Next we need to explore the mathematics of scaling.
Now you are ready to start subdividing your own shapes with more than 4 points!
How can trees be combined to count robots with many parts?
We need to be careful with the order of scaling and translation. But why?
Tree diagrams allow us to visualize these counting problems using any number of parts.
Next you'll use functions to *store* your deformer functions.
Okay we know how to calculate the touching point, great! Next let's think about how we can prove this is true.
Next let's build a blade of grass using a parabolic arc as a spine.
Created by Brit Cruise.
Let's breathe some life into our ball using a key animation principle: squash and stretch.
Now let's think about how subdivision would work in 3D.
Next we need to throw away the slope-intercept form and use the line equation instead.
Bonus! In this video we'll connect the degree of these curves to the number of control points in the construction.